Two immiscible fluids are flowing between two infinitely long and wide parallel flat plates under steady conditions. The flow is incompressible and laminar. The upper plate moves to the right with a speed of U$0$

while the lower plate is stationary. There is no pressure gradient forcing the fluid to move within the channel. Assume that the effects of surface tension are negligible and that the interface is horizontal. The pressure at the lower plate is P$0$

Do not change the position of the coordinate system or any of the symbols.

a$)$ List all the assumptions stated in the question text. Add any additional assumptions you make to the list.

b$)$ Simplify the continuity and Navier$-$Stokes equations for both fluids to obtain the differential equations that describe the velocity and pressure distributions in the flow field. Indicate why each term you neglect is omitted during the simplification.

c$)$ Write the appropriate boundary conditions to find the pressure and velocity distributions for both fluids.

d$)$ Solve the relevant differential equations to find the velocity distributions in both fluids.

e$)$ Solve the relevant differential equations to find the pressure distributions in both fluids.

f$)$ Sketch the velocity distributions approximately on a diagram.